### Table of contents

### Is there a Difference? How to use ANOVA to Find Out

The ANOVAAn analysis tool in statistics called Analysis of Variance (... Learn More... F ratio example is the ratio of two mean square values. If the null hypothesisHypothesis testing definition A statistical hypothesis test ... Learn More... is true, you expect F to have a value close to 1.0. A large F ratio means that the variation among group means is more than you’d expect to see by chance.

Below is an example of how to calculate the F-Statistic for an ANOVA (Analysis of VarianceAn analysis tool in statistics called Analysis of Variance (... Learn More...):

A company produces bags of popped popcorn. The customer’s “Critical to QualityCritical to Quality (CTQ) in Six Sigma, Trees can help to un... Learn More... Requirement” is to have the least number of un-popped kernels in a bag. We are going to take data from three vendors to determine if there is a difference in the number of un-popped popcorn kernels between the vendors.

A Six Sigma Green BeltThe Six Sigma Green Belt is a certificate that professionals... Learn More... and his team are going to run a hypothesis testHypothesis testing definition A statistical hypothesis test ... Learn More... with the following settings:

- 1 FactorStatistics can be confusing as the term "factor" can have di... Learn More... or Variable (which is the type of Kernel)
- 3 Settings (which in this case are 3 different vendors)
- N = Sample SizeThe sample size is an important feature of any empirical stu... Learn More... of 25 for each vendor (for a total of 75 samples)

Degrees of Freedom (this is the statistical bank account that we have to contribute to)

- Degrees of Freedom of the Factor (Type of Kernel) = 3 Vendors – 1 (=2)
- Total Degrees of Freedom = Sample Size of 25 – 1 (=24)
- Degrees of Freedom of ErrorStatistics error The dual dimension of error statistics is p... Learn More... (or Unexplained) = DF Total – DF Factor (=22)

F-Statistic:

Degrees of Freedom for the Factor (2)/ Degrees of Freedom for the Unexplained (or Error) (22)= Critical F-Statistic (2/22)

Look this up in this table: (https://www.statsoft.com/textbook/distribution-tables/#f05)

If you look up a table of F-Values (we are going to say that we will test this at the significance levelStatistics level A statistics level is the value of input in... Learn More... of 0.05 (at 95% Confidence), so, therefore, we are willing to take only a 5% risk of being wrong) you will find that the:

If the Calculated F-Value is less than the Critical F-Statistic of 3.44, then we “Accept the Null HypothesisA statistical hypothesis is a hypothesis that is testabl... Learn More....”

- Null Hypothesis (H0): “There is no difference in the number of un-popped kernels between vendors”
- Alternative Hypothesis (Ha)An alternative hypothesis (Ha) states that there is a s... Learn More...: “There is a difference in the number of un-popped kernels between vendors”
- Alpha is 0.05

Note* The F statisticA Sample Statistic, and a Population Parameter A sample for... Learn More... must be used in combination with the P value when you are deciding if your overall results are significant. If you have a significant F Statistic, it doesn’t mean that all variables are significant. The F-Statistic might be indicating that one is different. There might not be enough difference to cause the Statistical Validity of the test to be questioned.

Here is a resource for the Table with the Critical F-Statistic Values:

https://www.statsoft.com/textbook/distribution-tables/#f05